{
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    "# The Mathematical Engineering of Deep Learning\n",
    "\n",
    "## Practical 4 (Julia version)\n",
    "**For an R or Python version see the [course website](https://deeplearningmath.org/)**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Goals\n",
    "\n",
    "In this tutorial, we mainly use the MNIST dataset to explore classification using deep neural networks (DNN) models.\n",
    "At the end of this tutorial, you should be comfortable to use a software package (here `Flux.jl`) to run different models for a classification task.  You will explore different models by exploring/tuning different hyperparamaters of the DNN: \n",
    "\n",
    "- number of layers and nodes\n",
    "- batch normalization\n",
    "- regularization technique\n",
    "- dropout \n",
    "- weight initialization\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# MNIST"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Reminder**: Keep in mind that all features need to be numeric for running a feedforward DNN. When you have some categorical features you have to transform into numerical values such as one-hot encoded. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Flux.Data.MNIST\n",
    "\n",
    "trainLabels = MNIST.labels()\n",
    "trainImgs = MNIST.images()\n",
    "\n",
    "testLabels = MNIST.labels(:test)\n",
    "testImgs = MNIST.images(:test);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "trainLabels[1] = 5\n"
     ]
    },
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       "<rect width=\".81\" height=\".81\" x=\"27\" y=\"27\" fill=\"#000000\" />\n",
       "</svg>"
      ],
      "text/plain": [
       "28×28 Array{Gray{N0f8},2} with eltype ColorTypes.Gray{FixedPointNumbers.Normed{UInt8,8}}:\n",
       " Gray{N0f8}(0.0)  Gray{N0f8}(0.0)  …  Gray{N0f8}(0.0)  Gray{N0f8}(0.0)\n",
       " Gray{N0f8}(0.0)  Gray{N0f8}(0.0)     Gray{N0f8}(0.0)  Gray{N0f8}(0.0)\n",
       " Gray{N0f8}(0.0)  Gray{N0f8}(0.0)     Gray{N0f8}(0.0)  Gray{N0f8}(0.0)\n",
       " Gray{N0f8}(0.0)  Gray{N0f8}(0.0)     Gray{N0f8}(0.0)  Gray{N0f8}(0.0)\n",
       " Gray{N0f8}(0.0)  Gray{N0f8}(0.0)     Gray{N0f8}(0.0)  Gray{N0f8}(0.0)\n",
       " Gray{N0f8}(0.0)  Gray{N0f8}(0.0)  …  Gray{N0f8}(0.0)  Gray{N0f8}(0.0)\n",
       " Gray{N0f8}(0.0)  Gray{N0f8}(0.0)     Gray{N0f8}(0.0)  Gray{N0f8}(0.0)\n",
       " Gray{N0f8}(0.0)  Gray{N0f8}(0.0)     Gray{N0f8}(0.0)  Gray{N0f8}(0.0)\n",
       " Gray{N0f8}(0.0)  Gray{N0f8}(0.0)     Gray{N0f8}(0.0)  Gray{N0f8}(0.0)\n",
       " Gray{N0f8}(0.0)  Gray{N0f8}(0.0)     Gray{N0f8}(0.0)  Gray{N0f8}(0.0)\n",
       " Gray{N0f8}(0.0)  Gray{N0f8}(0.0)  …  Gray{N0f8}(0.0)  Gray{N0f8}(0.0)\n",
       " Gray{N0f8}(0.0)  Gray{N0f8}(0.0)     Gray{N0f8}(0.0)  Gray{N0f8}(0.0)\n",
       " Gray{N0f8}(0.0)  Gray{N0f8}(0.0)     Gray{N0f8}(0.0)  Gray{N0f8}(0.0)\n",
       " ⋮                                 ⋱                   \n",
       " Gray{N0f8}(0.0)  Gray{N0f8}(0.0)     Gray{N0f8}(0.0)  Gray{N0f8}(0.0)\n",
       " Gray{N0f8}(0.0)  Gray{N0f8}(0.0)     Gray{N0f8}(0.0)  Gray{N0f8}(0.0)\n",
       " Gray{N0f8}(0.0)  Gray{N0f8}(0.0)     Gray{N0f8}(0.0)  Gray{N0f8}(0.0)\n",
       " Gray{N0f8}(0.0)  Gray{N0f8}(0.0)     Gray{N0f8}(0.0)  Gray{N0f8}(0.0)\n",
       " Gray{N0f8}(0.0)  Gray{N0f8}(0.0)  …  Gray{N0f8}(0.0)  Gray{N0f8}(0.0)\n",
       " Gray{N0f8}(0.0)  Gray{N0f8}(0.0)     Gray{N0f8}(0.0)  Gray{N0f8}(0.0)\n",
       " Gray{N0f8}(0.0)  Gray{N0f8}(0.0)     Gray{N0f8}(0.0)  Gray{N0f8}(0.0)\n",
       " Gray{N0f8}(0.0)  Gray{N0f8}(0.0)     Gray{N0f8}(0.0)  Gray{N0f8}(0.0)\n",
       " Gray{N0f8}(0.0)  Gray{N0f8}(0.0)     Gray{N0f8}(0.0)  Gray{N0f8}(0.0)\n",
       " Gray{N0f8}(0.0)  Gray{N0f8}(0.0)  …  Gray{N0f8}(0.0)  Gray{N0f8}(0.0)\n",
       " Gray{N0f8}(0.0)  Gray{N0f8}(0.0)     Gray{N0f8}(0.0)  Gray{N0f8}(0.0)\n",
       " Gray{N0f8}(0.0)  Gray{N0f8}(0.0)     Gray{N0f8}(0.0)  Gray{N0f8}(0.0)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@show trainLabels[1]\n",
    "trainImgs[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Scale the data set\n",
    "\n",
    "The data is in gray scale with each image having 0 to 255 values. In general we would need to scale it, but Julia does this for us..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array{ColorTypes.Gray{FixedPointNumbers.Normed{UInt8,8}},2}"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "typeof(trainImgs[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0f0, 1.0f0)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "extrema(Float32.(trainImgs[1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Transform the outcome \n",
    "\n",
    "For multi-classification model (multinomial response 0 to 9), `Flux.jl` uses one-hot encoded for the outcome\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Flux: onehotbatch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "search:\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "\\begin{verbatim}\n",
       "onehotbatch(ls, labels[, unk...])\n",
       "\\end{verbatim}\n",
       "Return a \\texttt{OneHotMatrix} where \\texttt{k}th column of the matrix is \\texttt{onehot(ls[k], labels)}.\n",
       "\n",
       "If one of the input labels \\texttt{ls} is not found in \\texttt{labels} and \\texttt{unk} is given, return \\href{@ref}{\\texttt{onehot(unk, labels)}} ; otherwise the function will raise an error.\n",
       "\n",
       "\\section{Examples}\n",
       "\\begin{verbatim}\n",
       "julia> Flux.onehotbatch([:b, :a, :b], [:a, :b, :c])\n",
       "3×3 Flux.OneHotMatrix{Array{Flux.OneHotVector,1}}:\n",
       " 0  1  0\n",
       " 1  0  1\n",
       " 0  0  0\n",
       "\\end{verbatim}\n"
      ],
      "text/markdown": [
       "```\n",
       "onehotbatch(ls, labels[, unk...])\n",
       "```\n",
       "\n",
       "Return a `OneHotMatrix` where `k`th column of the matrix is `onehot(ls[k], labels)`.\n",
       "\n",
       "If one of the input labels `ls` is not found in `labels` and `unk` is given, return [`onehot(unk, labels)`](@ref) ; otherwise the function will raise an error.\n",
       "\n",
       "# Examples\n",
       "\n",
       "```jldoctest\n",
       "julia> Flux.onehotbatch([:b, :a, :b], [:a, :b, :c])\n",
       "3×3 Flux.OneHotMatrix{Array{Flux.OneHotVector,1}}:\n",
       " 0  1  0\n",
       " 1  0  1\n",
       " 0  0  0\n",
       "```\n"
      ],
      "text/plain": [
       "\u001b[36m  onehotbatch(ls, labels[, unk...])\u001b[39m\n",
       "\n",
       "  Return a \u001b[36mOneHotMatrix\u001b[39m where \u001b[36mk\u001b[39mth column of the matrix is \u001b[36monehot(ls[k],\n",
       "  labels)\u001b[39m.\n",
       "\n",
       "  If one of the input labels \u001b[36mls\u001b[39m is not found in \u001b[36mlabels\u001b[39m and \u001b[36munk\u001b[39m is given,\n",
       "  return \u001b[36monehot(unk, labels)\u001b[39m ; otherwise the function will raise an error.\n",
       "\n",
       "\u001b[1m  Examples\u001b[22m\n",
       "\u001b[1m  ≡≡≡≡≡≡≡≡≡≡\u001b[22m\n",
       "\n",
       "\u001b[36m  julia> Flux.onehotbatch([:b, :a, :b], [:a, :b, :c])\u001b[39m\n",
       "\u001b[36m  3×3 Flux.OneHotMatrix{Array{Flux.OneHotVector,1}}:\u001b[39m\n",
       "\u001b[36m   0  1  0\u001b[39m\n",
       "\u001b[36m   1  0  1\u001b[39m\n",
       "\u001b[36m   0  0  0\u001b[39m"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "? onehotbatch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10×60000 Flux.OneHotMatrix{Array{Flux.OneHotVector,1}}:\n",
       " 0  1  0  0  0  0  0  0  0  0  0  0  0  …  0  0  0  0  0  0  0  0  0  0  0  0\n",
       " 0  0  0  1  0  0  1  0  1  0  0  0  0     0  0  0  0  0  0  1  0  0  0  0  0\n",
       " 0  0  0  0  0  1  0  0  0  0  0  0  0     0  0  0  1  0  0  0  0  0  0  0  0\n",
       " 0  0  0  0  0  0  0  1  0  0  1  0  1     0  0  0  0  0  0  0  0  1  0  0  0\n",
       " 0  0  1  0  0  0  0  0  0  1  0  0  0     0  0  0  0  0  0  0  0  0  0  0  0\n",
       " 1  0  0  0  0  0  0  0  0  0  0  1  0  …  0  0  0  0  0  1  0  0  0  1  0  0\n",
       " 0  0  0  0  0  0  0  0  0  0  0  0  0     0  0  0  0  0  0  0  0  0  0  1  0\n",
       " 0  0  0  0  0  0  0  0  0  0  0  0  0     1  0  0  0  0  0  0  0  0  0  0  0\n",
       " 0  0  0  0  0  0  0  0  0  0  0  0  0     0  1  0  0  0  0  0  1  0  0  0  1\n",
       " 0  0  0  0  1  0  0  0  0  0  0  0  0     0  0  1  0  1  0  0  0  0  0  0  0"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "onehotbatch(trainLabels,0:9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Organize the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(Float32[0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0; … ; 0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0]\n",
       "\n",
       "Float32[0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0; … ; 0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0]\n",
       "\n",
       "Float32[0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0; … ; 0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0]\n",
       "\n",
       "...\n",
       "\n",
       "Float32[0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0; … ; 0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0]\n",
       "\n",
       "Float32[0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0; … ; 0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0]\n",
       "\n",
       "Float32[0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0; … ; 0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0], Bool[0 0 … 0 0; 0 0 … 0 0; … ; 0 0 … 0 1; 0 0 … 0 0])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "batchSize = 128\n",
    "validateFraction = 0.2\n",
    "numTrain = length(trainImgs)\n",
    "trainRange, validateRange = 1:Int(numTrain*(1-validateFraction)), (Int(numTrain*(1-validateFraction))+1):60000\n",
    "\n",
    "function minibatch(x, y, indexRange)\n",
    "    xBatch = Array{Float32}(undef, size(x[1])..., 1, length(indexRange))\n",
    "    for i in 1:length(indexRange)\n",
    "        xBatch[:, :, :, i] = Float32.(x[indexRange[i]])\n",
    "    end\n",
    "    return (xBatch, onehotbatch(y[indexRange], 0:9))#A tuple of x and y\n",
    "end\n",
    "\n",
    "mbIdxs = Iterators.partition(1:length(trainImgs), batchSize)\n",
    "trainSet = [minibatch(trainImgs, trainLabels, bi) for bi in mbIdxs]\n",
    "oneBatchTrainSet =  minibatch(trainImgs, trainLabels, 1:length(trainImgs))\n",
    "\n",
    "validateLabels = MNIST.labels()[validateRange]\n",
    "validateImgs = MNIST.images()[validateRange]\n",
    "validateSet = minibatch(validateImgs, validateLabels, 1:length(validateImgs))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Implementation a DNN using `Flux.jl`\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Flux, Flux.Data.MNIST, Statistics, Random, Plots; pyplot()\n",
    "using Flux: onehotbatch, onecold, crossentropy\n",
    "Random.seed!(0);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Chain(flatten, Dense(784, 128, relu), Dense(128, 64, relu), Dense(64, 10), softmax)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = Chain(flatten, #Assumes 28x28 input\n",
    "             Dense(784, 128,relu),\n",
    "             Dense(128,64,relu),\n",
    "             Dense(64, 10), softmax)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "28×28×1×1 Array{Float32,4}:\n",
       "[:, :, 1, 1] =\n",
       " 0.946243   0.7907     0.861884   0.852015  …  0.278257   0.604954   0.380738\n",
       " 0.712817   0.829283   0.444507   0.281978     0.0945773  0.463909   0.827011\n",
       " 0.771833   0.316909   0.298908   0.959519     0.703244   0.101018   0.381261\n",
       " 0.551615   0.625084   0.758625   0.753537     0.685499   0.829299   0.375471\n",
       " 0.878935   0.235904   0.281674   0.93951      0.23076    0.386309   0.397365\n",
       " 0.325261   0.411175   0.285024   0.956632  …  0.569028   0.252429   0.982844\n",
       " 0.399314   0.123499   0.841863   0.150126     0.876755   0.435955   0.341883\n",
       " 0.456478   0.702414   0.650233   0.856102     0.285693   0.342283   0.785169\n",
       " 0.654267   0.139802   0.120753   0.845503     0.193181   0.484545   0.199155\n",
       " 0.47415    0.0309595  0.607563   0.758074     0.8021     0.411037   0.124417\n",
       " 0.217815   0.212991   0.934512   0.297939  …  0.573945   0.389403   0.826388\n",
       " 0.92346    0.217736   0.176698   0.970543     0.761146   0.38932    0.749438\n",
       " 0.254004   0.0453079  0.961399   0.559079     0.915039   0.0842912  0.260626\n",
       " ⋮                                          ⋱  ⋮                     \n",
       " 0.935582   0.188664   0.0170866  0.680278     0.997682   0.422589   0.841956\n",
       " 0.633149   0.657502   0.315908   0.346803     0.749238   0.825455   0.117459\n",
       " 0.443983   0.614879   0.587946   0.972786     0.0252866  0.784645   0.237855\n",
       " 0.685007   0.786656   0.880215   0.401772     0.120887   0.702397   0.367985\n",
       " 0.542508   0.0975635  0.787061   0.257428  …  0.690107   0.327581   0.584963\n",
       " 0.0190682  0.85662    0.707275   0.122591     0.282259   0.749909   0.600887\n",
       " 0.387608   0.712057   0.45223    0.617122     0.390822   0.989238   0.782609\n",
       " 0.985144   0.83392    0.140242   0.162611     0.446136   0.182496   0.980717\n",
       " 0.141013   0.322666   0.473939   0.903096     0.342379   0.803603   0.874597\n",
       " 0.680371   0.234853   0.111215   0.664216  …  0.833831   0.0314848  0.514988\n",
       " 0.0547915  0.131552   0.244053   0.878343     0.868739   0.9162     0.918805\n",
       " 0.416545   0.741904   0.961629   0.946898     0.294369   0.883231   0.54634"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "testImg = Array{Float32}(undef, 28, 28, 1, 1)\n",
    "rand!(testImg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10×1 Array{Float32,2}:\n",
       " 0.095702074\n",
       " 0.04671081\n",
       " 0.06676274\n",
       " 0.18147221\n",
       " 0.102281936\n",
       " 0.07037333\n",
       " 0.10051205\n",
       " 0.10796334\n",
       " 0.08588455\n",
       " 0.14233695"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model(testImg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "length(model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "784×1 Array{Float32,2}:\n",
       " 0.9462434\n",
       " 0.7128167\n",
       " 0.7718327\n",
       " 0.55161476\n",
       " 0.8789346\n",
       " 0.32526112\n",
       " 0.39931428\n",
       " 0.45647812\n",
       " 0.6542666\n",
       " 0.47415006\n",
       " 0.2178154\n",
       " 0.92346036\n",
       " 0.25400412\n",
       " ⋮\n",
       " 0.84195554\n",
       " 0.11745858\n",
       " 0.23785472\n",
       " 0.36798525\n",
       " 0.5849631\n",
       " 0.6008874\n",
       " 0.78260934\n",
       " 0.9807174\n",
       " 0.8745967\n",
       " 0.51498795\n",
       " 0.91880524\n",
       " 0.5463395"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model[1](testImg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "128×1 Array{Float32,2}:\n",
       " 0.36691636\n",
       " 0.0\n",
       " 0.0\n",
       " 0.0\n",
       " 0.5109769\n",
       " 0.08157738\n",
       " 0.0\n",
       " 0.0\n",
       " 0.0\n",
       " 0.0\n",
       " 0.0\n",
       " 0.8274336\n",
       " 0.0\n",
       " ⋮\n",
       " 0.0\n",
       " 0.0\n",
       " 0.30795157\n",
       " 0.0\n",
       " 0.0\n",
       " 0.0\n",
       " 0.0\n",
       " 0.0\n",
       " 0.0\n",
       " 0.27733633\n",
       " 0.0\n",
       " 0.0"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model[1:2](testImg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "64×1 Array{Float32,2}:\n",
       " 0.38039497\n",
       " 0.0\n",
       " 0.0\n",
       " 0.5597278\n",
       " 0.6048984\n",
       " 0.14824015\n",
       " 0.08934927\n",
       " 0.10504165\n",
       " 0.5831885\n",
       " 0.3151437\n",
       " 0.0\n",
       " 0.12264562\n",
       " 0.0\n",
       " ⋮\n",
       " 0.062375724\n",
       " 0.32191017\n",
       " 0.0\n",
       " 0.59699786\n",
       " 0.0\n",
       " 0.64053875\n",
       " 0.0\n",
       " 0.23409869\n",
       " 0.29942575\n",
       " 0.0\n",
       " 0.0\n",
       " 0.4456669"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model[1:3](testImg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10×1 Array{Float32,2}:\n",
       " -0.15263861\n",
       " -0.8699029\n",
       " -0.51273334\n",
       "  0.48722395\n",
       " -0.08614558\n",
       " -0.46006426\n",
       " -0.10360097\n",
       " -0.032086916\n",
       " -0.2608746\n",
       "  0.24431852"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model[1:4](testImg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10×1 Array{Float32,2}:\n",
       " 0.095702074\n",
       " 0.04671081\n",
       " 0.06676274\n",
       " 0.18147221\n",
       " 0.102281936\n",
       " 0.07037333\n",
       " 0.10051205\n",
       " 0.10796334\n",
       " 0.08588455\n",
       " 0.14233695"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model[1:5](testImg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0f0"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(ans)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Accuracy and loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "loss (generic function with 1 method)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accuracy(x, y, model) = mean(onecold(model(x)) .== onecold(y))\n",
    "loss(x, y, model) = crossentropy(model(x), y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1: Validation Accuracy: 0.96\n",
      "2: Validation Accuracy: 0.969\n",
      "3: Validation Accuracy: 0.979\n",
      "4: Validation Accuracy: 0.977\n",
      "5: Validation Accuracy: 0.979\n",
      "6: Validation Accuracy: 0.976\n",
      "7: Validation Accuracy: 0.987\n",
      "8: Validation Accuracy: 0.987\n",
      "9: Validation Accuracy: 0.985\n",
      "10: Validation Accuracy: 0.989\n",
      "11: Validation Accuracy: 0.982\n",
      "12: Validation Accuracy: 0.984\n",
      "13: Validation Accuracy: 0.987\n",
      "14: Validation Accuracy: 0.99\n",
      "15: Validation Accuracy: 0.989\n",
      "16: Validation Accuracy: 0.99\n",
      "17: Validation Accuracy: 0.991\n",
      "18: Validation Accuracy: 0.992\n",
      "19: Validation Accuracy: 0.991\n",
      "20: Validation Accuracy: 0.993\n",
      "21: Validation Accuracy: 0.986\n",
      "22: Validation Accuracy: 0.993\n",
      "23: Validation Accuracy: 0.99\n",
      "24: Validation Accuracy: 0.993\n",
      "25: Validation Accuracy: 0.993\n",
      "\n",
      "Final validation accuracy = 0.99275\n"
     ]
    }
   ],
   "source": [
    "η = 0.01\n",
    "\n",
    "function trainModel(model;epochs = 25,opt = ADAM(η),verbose = true)\n",
    "    trainingLosses, validationLosses = [], []\n",
    "    trainingAccuracy, validationAccuracy = [], []\n",
    "    function updateAfterEpcoh()\n",
    "        push!(trainingLosses, loss(oneBatchTrainSet..., model))\n",
    "        push!(validationLosses, loss(validateSet..., model))\n",
    "        push!(trainingAccuracy,accuracy(oneBatchTrainSet..., model))\n",
    "        push!(validationAccuracy,accuracy(validateSet..., model))\n",
    "    end\n",
    "\n",
    "    model(trainSet[1][1]) #speedup by running once\n",
    "    for ep in 1:epochs\n",
    "        Flux.train!((x,y)->loss(x,y,model), params(model), trainSet, opt)\n",
    "        updateAfterEpcoh()\n",
    "        verbose && println(\"$(ep): Validation Accuracy: $(round(last(validationAccuracy),digits=3))\")\n",
    "    end\n",
    "    return (trainingLosses, validationLosses, trainingAccuracy, validationAccuracy)\n",
    "end\n",
    "\n",
    "traces = trainModel(model)\n",
    "println(\"\\nFinal validation accuracy = \", accuracy(validateSet..., model))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function plotModel(traces)\n",
    "    trainingLosses, validationLosses = traces[1], traces[2]\n",
    "    trainingAccuracy, validationAccuracy = traces[3], traces[4]\n",
    "\n",
    "    p1 = plot(trainingLosses,label=\"Train\", ylim=(0.0,0.5), xlabel=\"Epoch\", \n",
    "            ylabel = \"Loss\",c=:orange,seriestype = [:scatter,:line])\n",
    "         plot!(validationLosses,label=\"Validation\",c=:blue,seriestype = [:scatter,:line])\n",
    "\n",
    "    p2 = plot(trainingAccuracy,label=\"Train\", ylim=(0.9,1.0), xlabel=\"Epoch\", \n",
    "            ylabel = \"Accuracy\",legend=false,c=:orange,seriestype = [:scatter,:line])\n",
    "         plot!(validationAccuracy,label=\"Validation\",c=:blue,seriestype = [:scatter,:line])\n",
    "\n",
    "    plot(p1,p2,layout=(2,1),size=(500,400))\n",
    "end\n",
    "\n",
    "plotModel(traces)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that the loss function improves rapidly. However, we can see a potential overfit after 10 epochs. Indeed, the accurary rate of the validation set presents a flat shape after 10 epochs."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Considering the test set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
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       "</svg>"
      ],
      "text/plain": [
       "28×28 Array{Gray{N0f8},2} with eltype Gray{FixedPointNumbers.Normed{UInt8,8}}:\n",
       " Gray{N0f8}(0.0)  Gray{N0f8}(0.0)  …  Gray{N0f8}(0.0)  Gray{N0f8}(0.0)\n",
       " Gray{N0f8}(0.0)  Gray{N0f8}(0.0)     Gray{N0f8}(0.0)  Gray{N0f8}(0.0)\n",
       " Gray{N0f8}(0.0)  Gray{N0f8}(0.0)     Gray{N0f8}(0.0)  Gray{N0f8}(0.0)\n",
       " Gray{N0f8}(0.0)  Gray{N0f8}(0.0)     Gray{N0f8}(0.0)  Gray{N0f8}(0.0)\n",
       " Gray{N0f8}(0.0)  Gray{N0f8}(0.0)     Gray{N0f8}(0.0)  Gray{N0f8}(0.0)\n",
       " Gray{N0f8}(0.0)  Gray{N0f8}(0.0)  …  Gray{N0f8}(0.0)  Gray{N0f8}(0.0)\n",
       " Gray{N0f8}(0.0)  Gray{N0f8}(0.0)     Gray{N0f8}(0.0)  Gray{N0f8}(0.0)\n",
       " Gray{N0f8}(0.0)  Gray{N0f8}(0.0)     Gray{N0f8}(0.0)  Gray{N0f8}(0.0)\n",
       " Gray{N0f8}(0.0)  Gray{N0f8}(0.0)     Gray{N0f8}(0.0)  Gray{N0f8}(0.0)\n",
       " Gray{N0f8}(0.0)  Gray{N0f8}(0.0)     Gray{N0f8}(0.0)  Gray{N0f8}(0.0)\n",
       " Gray{N0f8}(0.0)  Gray{N0f8}(0.0)  …  Gray{N0f8}(0.0)  Gray{N0f8}(0.0)\n",
       " Gray{N0f8}(0.0)  Gray{N0f8}(0.0)     Gray{N0f8}(0.0)  Gray{N0f8}(0.0)\n",
       " Gray{N0f8}(0.0)  Gray{N0f8}(0.0)     Gray{N0f8}(0.0)  Gray{N0f8}(0.0)\n",
       " ⋮                                 ⋱                   \n",
       " Gray{N0f8}(0.0)  Gray{N0f8}(0.0)     Gray{N0f8}(0.0)  Gray{N0f8}(0.0)\n",
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       " Gray{N0f8}(0.0)  Gray{N0f8}(0.0)  …  Gray{N0f8}(0.0)  Gray{N0f8}(0.0)\n",
       " Gray{N0f8}(0.0)  Gray{N0f8}(0.0)     Gray{N0f8}(0.0)  Gray{N0f8}(0.0)\n",
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       " Gray{N0f8}(0.0)  Gray{N0f8}(0.0)  …  Gray{N0f8}(0.0)  Gray{N0f8}(0.0)\n",
       " Gray{N0f8}(0.0)  Gray{N0f8}(0.0)     Gray{N0f8}(0.0)  Gray{N0f8}(0.0)\n",
       " Gray{N0f8}(0.0)  Gray{N0f8}(0.0)     Gray{N0f8}(0.0)  Gray{N0f8}(0.0)"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#creating a predictor function (packaging the neural network)\n",
    "exampleImage = testImgs[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "28×28×1×1 Array{Float32,4}:\n",
       "[:, :, 1, 1] =\n",
       " 0.0  0.0  0.0  0.0  0.0  0.0  0.0       …  0.0  0.0  0.0  0.0  0.0  0.0\n",
       " 0.0  0.0  0.0  0.0  0.0  0.0  0.0          0.0  0.0  0.0  0.0  0.0  0.0\n",
       " 0.0  0.0  0.0  0.0  0.0  0.0  0.0          0.0  0.0  0.0  0.0  0.0  0.0\n",
       " 0.0  0.0  0.0  0.0  0.0  0.0  0.0          0.0  0.0  0.0  0.0  0.0  0.0\n",
       " 0.0  0.0  0.0  0.0  0.0  0.0  0.0          0.0  0.0  0.0  0.0  0.0  0.0\n",
       " 0.0  0.0  0.0  0.0  0.0  0.0  0.0       …  0.0  0.0  0.0  0.0  0.0  0.0\n",
       " 0.0  0.0  0.0  0.0  0.0  0.0  0.0          0.0  0.0  0.0  0.0  0.0  0.0\n",
       " 0.0  0.0  0.0  0.0  0.0  0.0  0.329412     0.0  0.0  0.0  0.0  0.0  0.0\n",
       " 0.0  0.0  0.0  0.0  0.0  0.0  0.870588     0.0  0.0  0.0  0.0  0.0  0.0\n",
       " 0.0  0.0  0.0  0.0  0.0  0.0  0.262745     0.0  0.0  0.0  0.0  0.0  0.0\n",
       " 0.0  0.0  0.0  0.0  0.0  0.0  0.0       …  0.0  0.0  0.0  0.0  0.0  0.0\n",
       " 0.0  0.0  0.0  0.0  0.0  0.0  0.0          0.0  0.0  0.0  0.0  0.0  0.0\n",
       " 0.0  0.0  0.0  0.0  0.0  0.0  0.0          0.0  0.0  0.0  0.0  0.0  0.0\n",
       " ⋮                        ⋮              ⋱                 ⋮         \n",
       " 0.0  0.0  0.0  0.0  0.0  0.0  0.0          0.0  0.0  0.0  0.0  0.0  0.0\n",
       " 0.0  0.0  0.0  0.0  0.0  0.0  0.0          0.0  0.0  0.0  0.0  0.0  0.0\n",
       " 0.0  0.0  0.0  0.0  0.0  0.0  0.0          0.0  0.0  0.0  0.0  0.0  0.0\n",
       " 0.0  0.0  0.0  0.0  0.0  0.0  0.0          0.0  0.0  0.0  0.0  0.0  0.0\n",
       " 0.0  0.0  0.0  0.0  0.0  0.0  0.0       …  0.0  0.0  0.0  0.0  0.0  0.0\n",
       " 0.0  0.0  0.0  0.0  0.0  0.0  0.0          0.0  0.0  0.0  0.0  0.0  0.0\n",
       " 0.0  0.0  0.0  0.0  0.0  0.0  0.0          0.0  0.0  0.0  0.0  0.0  0.0\n",
       " 0.0  0.0  0.0  0.0  0.0  0.0  0.0          0.0  0.0  0.0  0.0  0.0  0.0\n",
       " 0.0  0.0  0.0  0.0  0.0  0.0  0.0          0.0  0.0  0.0  0.0  0.0  0.0\n",
       " 0.0  0.0  0.0  0.0  0.0  0.0  0.0       …  0.0  0.0  0.0  0.0  0.0  0.0\n",
       " 0.0  0.0  0.0  0.0  0.0  0.0  0.0          0.0  0.0  0.0  0.0  0.0  0.0\n",
       " 0.0  0.0  0.0  0.0  0.0  0.0  0.0          0.0  0.0  0.0  0.0  0.0  0.0"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "testImg = Array{Float32}(undef, 28, 28, 1, 1)\n",
    "testImg[:,:,1,1] = exampleImage;\n",
    "testImg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10×1 Array{Float32,2}:\n",
       " 6.085367f-19\n",
       " 3.2641642f-20\n",
       " 1.1675848f-12\n",
       " 8.938367f-16\n",
       " 8.878222f-15\n",
       " 1.4323898f-23\n",
       " 3.374141f-30\n",
       " 1.0\n",
       " 1.0915864f-21\n",
       " 2.6686948f-9"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "exampleModelOutput = model(testImg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "784×1 Array{Float32,2}:\n",
       " 0.0\n",
       " 0.0\n",
       " 0.0\n",
       " 0.0\n",
       " 0.0\n",
       " 0.0\n",
       " 0.0\n",
       " 0.0\n",
       " 0.0\n",
       " 0.0\n",
       " 0.0\n",
       " 0.0\n",
       " 0.0\n",
       " ⋮\n",
       " 0.0\n",
       " 0.0\n",
       " 0.0\n",
       " 0.0\n",
       " 0.0\n",
       " 0.0\n",
       " 0.0\n",
       " 0.0\n",
       " 0.0\n",
       " 0.0\n",
       " 0.0\n",
       " 0.0"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Another way is to put it in a 784x1 matrix/array\n",
    "testImg2 = reshape(Float32.(exampleImage),784,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10×1 Array{Float32,2}:\n",
       " 6.085367f-19\n",
       " 3.2641642f-20\n",
       " 1.1675848f-12\n",
       " 8.938367f-16\n",
       " 8.878222f-15\n",
       " 1.4323898f-23\n",
       " 3.374141f-30\n",
       " 1.0\n",
       " 1.0915864f-21\n",
       " 2.6686948f-9"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model(testImg2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Creating a predictor function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1-element Array{Int64,1}:\n",
       " 8"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "onecold(exampleModelOutput)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "first(onecold(exampleModelOutput)) - 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "predictor (generic function with 1 method)"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predictor(img,model) = first(onecold(model(reshape(Float32.(img),784,1))))-1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predictor(exampleImage,model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10000-element Array{Int64,1}:\n",
       " 7\n",
       " 2\n",
       " 1\n",
       " 0\n",
       " 4\n",
       " 1\n",
       " 4\n",
       " 9\n",
       " 5\n",
       " 9\n",
       " 0\n",
       " 6\n",
       " 9\n",
       " ⋮\n",
       " 5\n",
       " 6\n",
       " 7\n",
       " 8\n",
       " 9\n",
       " 0\n",
       " 1\n",
       " 2\n",
       " 3\n",
       " 4\n",
       " 5\n",
       " 6"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "preds = [predictor(img,model) for img in testImgs]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9716"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "testAccuracy = sum(preds .== testLabels)/length(preds)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10×10 Array{Int64,2}:\n",
       " 972     0     2    0    2    2    5    1    2    1\n",
       "   1  1126     0    0    0    1    4    3    1    2\n",
       "   0     3  1011    8    2    1    2   22    9    2\n",
       "   2     1     8  968    0    6    1    6   11    8\n",
       "   0     0     2    0  956    0    2    0    1   11\n",
       "   0     0     2   21    0  863   13    0    6    3\n",
       "   2     1     1    0    2    4  928    0    1    2\n",
       "   1     1     3    4    2    3    0  987    2    6\n",
       "   2     3     3    5    6   10    2    4  940    9\n",
       "   0     0     0    4   12    2    1    5    1  965"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "confusionMatrix = \n",
    "    [sum([predictor(img,model) .== i for img in testImgs[testLabels .== j]]) \n",
    "        for i in 0:9, j in 0:9]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9716"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using LinearAlgebra\n",
    "sum(diag(confusionMatrix))/length(preds)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Improve our model by tuning some parameters \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Model complexity\n",
    "\n",
    "We will explore different model size by playing with the number of hidden layer from 1 to 3 and different number of neurons. Complex models have higher capacity to learn more features and patterns in the data, however they can overfit the training data. We try to maximize a high validation performance while minimizing the complexity of our model. The folowing table present the 9 models we will explore:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3×3 Array{Array{Int64,1},2}:\n",
       " [16]   [16, 8]     [16, 8, 4]\n",
       " [64]   [64, 32]    [64, 32, 16]\n",
       " [256]  [256, 128]  [256, 128, 64]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "Chain(flatten, Dense(784, 64, relu), Dense(64, 32, relu), Dense(32, 16, relu), Dense(16, 10), softmax)"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sizes = [:small,:medium,:large]\n",
    "layers = [1,2,3]\n",
    "models = Dict{Tuple{Symbol,Int64},Array{Int64,1}}()\n",
    "models[(:small,1)] = [16] ; models[(:small,2)] = [16,8] ;  models[(:small,3)] = [16,8,4]\n",
    "models[(:medium,1)] = [64] ; models[(:medium,2)] = [64,32] ;  models[(:medium,3)] = [64,32,16]\n",
    "models[(:large,1)] = [256] ; models[(:large,2)] = [256,128] ;  models[(:large,3)] = [256,128,64]\n",
    "\n",
    "function makeModel(size,layers) \n",
    "    functions = []\n",
    "    push!(functions,flatten)\n",
    "    architecture = models[(size,layers)]\n",
    "    prevNeurons = 784\n",
    "    for l in 1:layers\n",
    "        neurons = architecture[l]\n",
    "        push!(functions,Dense(prevNeurons,neurons,relu))\n",
    "        prevNeurons = neurons\n",
    "    end\n",
    "    push!(functions,Dense(prevNeurons,10))\n",
    "    push!(functions,softmax)\n",
    "    Chain(functions...)\n",
    "end\n",
    "\n",
    "display([models[(s,l)] for s in sizes, l in layers])\n",
    "\n",
    "makeModel(:medium,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1: Validation Accuracy: 0.956\n",
      "2: Validation Accuracy: 0.978\n",
      "3: Validation Accuracy: 0.97\n",
      "4: Validation Accuracy: 0.979\n",
      "5: Validation Accuracy: 0.968\n"
     ]
    },
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = makeModel(:medium,2)\n",
    "traces = trainModel(model,epochs = 5)\n",
    "plotModel(traces)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Task 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Repeat it for the 2-layer and 3-layer model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Task 2\n",
    "\n",
    "What are you conclusions from this experiment ? which models present some overfit issue ? which models to keep ?\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Batch Normalization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "search: \u001b[0m\u001b[1mB\u001b[22m\u001b[0m\u001b[1ma\u001b[22m\u001b[0m\u001b[1mt\u001b[22m\u001b[0m\u001b[1mc\u001b[22m\u001b[0m\u001b[1mh\u001b[22m\u001b[0m\u001b[1mN\u001b[22m\u001b[0m\u001b[1mo\u001b[22m\u001b[0m\u001b[1mr\u001b[22m\u001b[0m\u001b[1mm\u001b[22m \u001b[0m\u001b[1mb\u001b[22m\u001b[0m\u001b[1ma\u001b[22m\u001b[0m\u001b[1mt\u001b[22m\u001b[0m\u001b[1mc\u001b[22m\u001b[0m\u001b[1mh\u001b[22med_tra\u001b[0m\u001b[1mn\u001b[22msp\u001b[0m\u001b[1mo\u001b[22mse\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "\\begin{verbatim}\n",
       "BatchNorm(channels::Integer, σ = identity;\n",
       "          initβ = zeros, initγ = ones,\n",
       "          ϵ = 1e-8, momentum = .1)\n",
       "\\end{verbatim}\n",
       "\\href{https://arxiv.org/abs/1502.03167}{Batch Normalization} layer. \\texttt{channels} should be the size of the channel dimension in your data (see below).\n",
       "\n",
       "Given an array with \\texttt{N} dimensions, call the \\texttt{N-1}th the channel dimension. (For a batch of feature vectors this is just the data dimension, for \\texttt{WHCN} images it's the usual channel dimension.)\n",
       "\n",
       "\\texttt{BatchNorm} computes the mean and variance for each each \\texttt{W×H×1×N} slice and shifts them to have a new mean and variance (corresponding to the learnable, per-channel \\texttt{bias} and \\texttt{scale} parameters).\n",
       "\n",
       "Use \\href{@ref}{\\texttt{testmode!}} during inference.\n",
       "\n",
       "\\section{Examples}\n",
       "\\begin{verbatim}\n",
       "m = Chain(\n",
       "  Dense(28^2, 64),\n",
       "  BatchNorm(64, relu),\n",
       "  Dense(64, 10),\n",
       "  BatchNorm(10),\n",
       "  softmax)\n",
       "\\end{verbatim}\n"
      ],
      "text/markdown": [
       "```\n",
       "BatchNorm(channels::Integer, σ = identity;\n",
       "          initβ = zeros, initγ = ones,\n",
       "          ϵ = 1e-8, momentum = .1)\n",
       "```\n",
       "\n",
       "[Batch Normalization](https://arxiv.org/abs/1502.03167) layer. `channels` should be the size of the channel dimension in your data (see below).\n",
       "\n",
       "Given an array with `N` dimensions, call the `N-1`th the channel dimension. (For a batch of feature vectors this is just the data dimension, for `WHCN` images it's the usual channel dimension.)\n",
       "\n",
       "`BatchNorm` computes the mean and variance for each each `W×H×1×N` slice and shifts them to have a new mean and variance (corresponding to the learnable, per-channel `bias` and `scale` parameters).\n",
       "\n",
       "Use [`testmode!`](@ref) during inference.\n",
       "\n",
       "# Examples\n",
       "\n",
       "```julia\n",
       "m = Chain(\n",
       "  Dense(28^2, 64),\n",
       "  BatchNorm(64, relu),\n",
       "  Dense(64, 10),\n",
       "  BatchNorm(10),\n",
       "  softmax)\n",
       "```\n"
      ],
      "text/plain": [
       "\u001b[36m  BatchNorm(channels::Integer, σ = identity;\u001b[39m\n",
       "\u001b[36m            initβ = zeros, initγ = ones,\u001b[39m\n",
       "\u001b[36m            ϵ = 1e-8, momentum = .1)\u001b[39m\n",
       "\n",
       "  Batch Normalization (https://arxiv.org/abs/1502.03167) layer. \u001b[36mchannels\u001b[39m\n",
       "  should be the size of the channel dimension in your data (see below).\n",
       "\n",
       "  Given an array with \u001b[36mN\u001b[39m dimensions, call the \u001b[36mN-1\u001b[39mth the channel dimension. (For\n",
       "  a batch of feature vectors this is just the data dimension, for \u001b[36mWHCN\u001b[39m images\n",
       "  it's the usual channel dimension.)\n",
       "\n",
       "  \u001b[36mBatchNorm\u001b[39m computes the mean and variance for each each \u001b[36mW×H×1×N\u001b[39m slice and\n",
       "  shifts them to have a new mean and variance (corresponding to the learnable,\n",
       "  per-channel \u001b[36mbias\u001b[39m and \u001b[36mscale\u001b[39m parameters).\n",
       "\n",
       "  Use \u001b[36mtestmode!\u001b[39m during inference.\n",
       "\n",
       "\u001b[1m  Examples\u001b[22m\n",
       "\u001b[1m  ≡≡≡≡≡≡≡≡≡≡\u001b[22m\n",
       "\n",
       "\u001b[36m  m = Chain(\u001b[39m\n",
       "\u001b[36m    Dense(28^2, 64),\u001b[39m\n",
       "\u001b[36m    BatchNorm(64, relu),\u001b[39m\n",
       "\u001b[36m    Dense(64, 10),\u001b[39m\n",
       "\u001b[36m    BatchNorm(10),\u001b[39m\n",
       "\u001b[36m    softmax)\u001b[39m"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "? BatchNorm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1: Validation Accuracy: 0.97\n",
      "2: Validation Accuracy: 0.984\n",
      "3: Validation Accuracy: 0.987\n",
      "4: Validation Accuracy: 0.987\n",
      "5: Validation Accuracy: 0.989\n",
      "6: Validation Accuracy: 0.99\n",
      "7: Validation Accuracy: 0.991\n",
      "8: Validation Accuracy: 0.993\n",
      "9: Validation Accuracy: 0.993\n",
      "10: Validation Accuracy: 0.995\n",
      "11: Validation Accuracy: 0.993\n",
      "12: Validation Accuracy: 0.993\n",
      "13: Validation Accuracy: 0.993\n",
      "14: Validation Accuracy: 0.994\n",
      "15: Validation Accuracy: 0.991\n",
      "16: Validation Accuracy: 0.995\n",
      "17: Validation Accuracy: 0.995\n",
      "18: Validation Accuracy: 0.997\n",
      "19: Validation Accuracy: 0.995\n",
      "20: Validation Accuracy: 0.995\n",
      "21: Validation Accuracy: 0.996\n",
      "22: Validation Accuracy: 0.996\n",
      "23: Validation Accuracy: 0.992\n",
      "24: Validation Accuracy: 0.994\n",
      "25: Validation Accuracy: 0.997\n",
      "\n",
      "Final validation accuracy = 0.9969166666666667\n"
     ]
    }
   ],
   "source": [
    "model= Chain(flatten, \n",
    "             Dense(784, 128,relu),\n",
    "             BatchNorm(128),\n",
    "             Dense(128,64,relu),\n",
    "             BatchNorm(64),\n",
    "             Dense(64, 10), softmax)\n",
    "traces = trainModel(model)\n",
    "println(\"\\nFinal validation accuracy = \", accuracy(validateSet..., model))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9774"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "preds = [predictor(img,model) for img in testImgs]\n",
    "testAccuracy = sum(preds .== testLabels)/length(preds)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Regularization\n",
    "\n",
    "Regularization is generally a good practice for overfitting issue. Here we explore $L_1$ and $L_2$ normalization:\n",
    "\n",
    "Here the code for a model with batch normalization and $L_2$ regularization.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#QQQQ to do"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task\n",
    "\n",
    "Present the result of the model with 3-layer with 256, 128 and 64 nodes per respective layer, with batch normalization  and with $L_2$ regularization components. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dropout\n",
    "\n",
    "An another avenue for overfitting issue is to use the **dropout** strategy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# QQQQ\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## What about the initialization of the weight\n",
    "\n",
    "Keep in mind that weight initialization can have an impact on both the convergence rate and\n",
    "the accuracy of your network. In **Keras**, the argument **kernel_initializer** in the function **layer_dense** allows us to set up different weight initialization. The default is the \"Glorot uniform\" which draws samples from a uniform within $[-a,a]$ where $a=\\sqrt{\\frac{6}{(fan_i+fan_o)}}$ where $fan_i$ is the number of inputs in the weight tensor and $fan_o$ is the number of output in the weight tensor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# QQQQ\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Early stop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#QQQQ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Final Task"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Present the performance of your final model on the test set:\n",
    "\n",
    "- confusion matrix\n",
    "- accuracy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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